Emphasizes a strong romantic interest, suggesting that the person is ignoring others. Despite the many eligible bachelors, she only has eyes for John.
Pro Tip 2/3
Exclusivity
Implies that no one else is being considered in a romantic context. He's asked out many women, but he only has eyes for his childhood sweetheart.
Pro Tip 3/3
Literal Usage
Not actually about sight, but rather attention or affection towards someone. Even in a crowded room, it's obvious that she only has eyes for her partner.